Normally it wont take more than couple of days or maximum a week.
but your case you and your husband are in different sponsorship.
first, who is going to sponsor your baby you or your husband. both can sponsor but need to produce required document correctly.
dox needed: NOC Letter and Salary certificate from company, birth certificate & passport copy of your baby and passport copy + QID of the sponsor (you / your husband).Marriage certificate with proper attestation. this is what my friend did in just last month. and make the visa ASAP other wise HMC will not give the vaccine for your baby from 2nd month. so make it urgent.